fix: remove intermittently failing ecdsa mul test

[suyash67]

Overview

I had added a test that checked if secp256k1_ecdsa_mul correctly returned point at infinity when we have private key $x$ defined as:

$$x = - u_1 \cdot u_2^{-1}$$

which would mean the scalar multiplication $(u_1 \cdot G + u_2 \cdot Q) = \mathcal{O}$ would result in a point at infinity. However, since the Montgomery ladder does not handle points at infinity (for efficiency purposes, we use incomplete addition formulae in the ladder computation), the circuit can fail by hitting a point at infinity during the ladder computation. Thus, this test was hitting intermittent failure (crash) once in a while. It is best to remove this test as we do not intend for Montgomery ladder to handle intermediate points at infinity.

As a side note, the test should not have been crashing and should gracefully fail at an assertion (with circuit failure). I've fixed this minor issue in bigfield and added a test in biggroup to catch the circuit failure.

Point at Infinity in Montgomery Ladder

At round $i$ of the iterative wNAF-style MSM, the partial accumulator has the form

$R_i = \sum_{k<i} 2^{e_k} \Big(u_{2,lo}[k] \cdot Q + u_{2,hi}[k] \cdot (\lambda Q)\Big) + \sum_{k<i} 2^{f_k}\Big(u_{1,lo}[k] \cdot G + u_{1,hi}[k] \cdot (\lambda G)\Big)$

Grouping terms, this is always expressible as

$$ R_i = U_i Q + V_i G, $$

where

$U_i=\sum_{k<i}2^{e_k}(u_{2,lo,k} + \lambda \cdot u_{2,hi,k})$

$V_i=\sum_{k<i}2^{f_k}(u_{1,lo,k} + \lambda \cdot u_{1,hi,k}).$

Writing the public key as $Q=xG$, we get

$$ R_i=(U_i x + V_i)G. $$

Therefore an intermediate infinity occurs exactly when

$$ R_i=\mathcal{O} \iff U_i x + V_i \equiv 0 \pmod n. $$

Since the wNAF slice digits $u_{1,lo},u_{1,hi},u_{2,lo},u_{2,hi} \in [ \pm1,\pm3,\pm5,\pm7 ]$ are signed, partial sums may cancel, so intermediate iterates $R_i$ may legitimately equal the point at infinity even if the final result is nonzero.

[federicobarbacovi]

Looks good, thanks for doing this!